Advances in Condensed Matter Physics
Volume 2014, Article ID 373674, 7 pages
http://dx.doi.org/10.1155/2014/373674
Numerical Study of Membrane Configurations
1Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, SI-1000 Ljubljana, Slovenia
2Laboratory of Clinical Biophysics, Faculty of Health Sciences, University of Ljubljana, Zdravstvena 5, SI-1000 Ljubljana, Slovenia
3Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, SI-2000 Maribor, Slovenia
4Jožef Stefan Institute, P.O. Box 3000, SI-1000 Ljubljana, Slovenia
5Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
Received 3 August 2014; Accepted 6 October 2014; Published 30 November 2014
Academic Editor: George Cordoyiannis
Copyright © 2014 Luka Mesarec et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- H. J. Deuling and W. Helfrich, “Red blood cell shapes as explained on the basis of curvature elasticity,” Biophysical Journal, vol. 16, no. 8, pp. 861–868, 1976. View at Publisher · View at Google Scholar · View at Scopus
- B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell, Garland Science, New York, NY, USA, 2008.
- H. J. Gao, W. D. Shi, and L. B. Freund, “Mechanics of receptor-mediated endocytosis,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 27, pp. 9469–9474, 2005. View at Publisher · View at Google Scholar · View at Scopus
- G. J. Doherty and H. T. McMahon, “Mechanisms of endocytosis,” Annual Review of Biochemistry, vol. 78, pp. 857–902, 2009. View at Publisher · View at Google Scholar · View at Scopus
- E. Sackmann, “Molecular and global structure and dynamics of membranes and lipid bilayers,” Canadian Journal of Physics, vol. 68, no. 9, pp. 999–1012, 1990. View at Google Scholar
- R. Lipowsky and E. Sackmann, Structure and Dynamics of Membranes: I. From Cells to Vesicles/II. Generic and Specific Interactions, Elsevier, New York, NY, USA, 1995.
- M. B. Schneider, J. T. Jenkins, and W. W. Webb, “Thermal fluctuations of large cylindrical phospholipid vesicles.,” Biophysical Journal, vol. 45, no. 5, pp. 891–899, 1984. View at Publisher · View at Google Scholar · View at Scopus
- D. R. Nelson, “Toward a tetravalent chemistry of colloids,” Nano Letters, vol. 2, no. 10, pp. 1125–1129, 2002. View at Publisher · View at Google Scholar · View at Scopus
- V. Vitelli and A. M. Turner, “Anomalous coupling between topological defects and curvature,” Physical Review Letters, vol. 93, no. 21, Article ID 215301, 2004. View at Publisher · View at Google Scholar · View at Scopus
- F. C. MacKintosh and T. C. Lubensky, “Orientational order, topology, and vesicle shapes,” Physical Review Letters, vol. 67, no. 9, pp. 1169–1172, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- S. Kralj, R. Rosso, and E. G. Virga, “Curvature control of valence on nematic shells,” Soft Matter, vol. 7, no. 2, pp. 670–683, 2011. View at Publisher · View at Google Scholar · View at Scopus
- R. L. B. Selinger, A. Konya, A. Travesset, and J. V. Selinger, “Monte Carlo studies of the XY model on two-dimensional curved surfaces,” Journal of Physical Chemistry B, vol. 115, no. 48, pp. 13989–13993, 2011. View at Publisher · View at Google Scholar · View at Scopus
- T.-S. Nguyen, J. Geng, R. L. B. Selinger, and J. V. Selinger, “Nematic order on a deformable vesicle: theory and simulation,” Soft Matter, vol. 9, no. 34, pp. 8314–8326, 2013. View at Publisher · View at Google Scholar · View at Scopus
- M. A. Bates, G. Skačej, and C. Zannoni, “Defects and ordering in nematic coatings on uniaxial and biaxial colloids,” Soft Matter, vol. 6, no. 3, pp. 655–663, 2010. View at Publisher · View at Google Scholar · View at Scopus
- V. Vitelli and D. R. Nelson, “Nematic textures in spherical shells,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 74, no. 2, Article ID 021711, 18 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- A. Fernández-Nieves, V. Vitelli, A. S. Utada et al., “Novel defect structures in nematic liquid crystal shells,” Physical Review Letters, vol. 99, no. 15, Article ID 157801, 2007. View at Publisher · View at Google Scholar · View at Scopus
- W. Helfrich, “Elastic properties of lipid bilayers: theory and possible experiments,” Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie, vol. 28, no. 11, pp. 693–703, 1973. View at Google Scholar · View at Scopus
- E. A. Evans, “Bending resistance and chemically induced moments in membrane bilayers,” Biophysical Journal, vol. 14, no. 12, pp. 923–931, 1974. View at Publisher · View at Google Scholar · View at Scopus
- Z. Shi and T. Baumgart, “Dynamics and instabilities of lipid bilayer membrane shapes,” Advances in Colloid and Interface Science, vol. 208, pp. 76–88, 2014. View at Publisher · View at Google Scholar · View at Scopus
- A. Boulbitch, R. Simson, D. A. Simson et al., “Shape instability of a biomembrane driven by a local softening of the underlying actin cortex,” Physical Review E, vol. 62, no. 3, pp. 3974–3985, 2000. View at Publisher · View at Google Scholar · View at Scopus
- V. Kralj-Iglic, A. Iglic, G. Gomiscek, F. Sevsek, V. Arrigler, and H. Hägerstrand, “Microtubes and nanotubes of a phospholipid bilayer membrane,” Journal of Physics A: Mathematical and General, vol. 35, no. 7, pp. 1533–1549, 2002. View at Publisher · View at Google Scholar · View at Scopus
- V. Kralj-Iglič, B. Babnik, D. R. Gauger, S. May, and A. Iglič, “Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles,” Journal of Statistical Physics, vol. 125, no. 3, pp. 723–752, 2006. View at Publisher · View at Google Scholar · View at Scopus
- V. Vitkova, D. Mitkova, A. Stoyanova-Ivanova, N. Kozarev, and I. Bivas, “Bending rigidity of lipid membranes and the ph of aqueous surroundings,” Comptes Rendus de L'Academie Bulgare des Sciences, vol. 65, no. 3, pp. 329–334, 2012. View at Google Scholar · View at Scopus
- R. Dimova, “Recent developments in the field of bending rigidity measurements on membranes,” Advances in Colloid and Interface Science, vol. 208, pp. 225–234, 2014. View at Publisher · View at Google Scholar · View at Scopus
- P. B. Canham, “The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell,” Journal of Theoretical Biology, vol. 26, no. 1, pp. 61–76, 1970. View at Publisher · View at Google Scholar · View at Scopus
- W. T. Góźdź, “Influence of spontaneous curvature and microtubules on the conformations of lipid vesicles,” Journal of Physical Chemistry B, vol. 109, no. 44, pp. 21145–21149, 2005. View at Publisher · View at Google Scholar · View at Scopus
- W. T. Góźdź, “Spontaneous curvature induced shape transformations of tubular polymersomes,” Langmuir, vol. 20, no. 18, pp. 7385–7391, 2004. View at Publisher · View at Google Scholar · View at Scopus
- W. T. Góźdź, “The interface width of separated two-component lipid membranes,” Journal of Physical Chemistry B, vol. 110, no. 43, pp. 21981–21986, 2006. View at Publisher · View at Google Scholar · View at Scopus
- G. Gompper and D. M. Kroll, “Triangula ted-surface models of uctuating membranes,” in Statistical Mechanics of Membranes and Surfaces, D. Nelson, T. Piran, and S. Weinberg, Eds., pp. 359–426, World Scientific, Singapore, 2nd edition, 2004. View at Google Scholar
- G. Gompper and D. M. Kroll, “Random surface discretization and the renormalization of the bending rigidity,” Journal de Physique I, vol. 6, no. 10, pp. 1305–1320, 1996. View at Publisher · View at Google Scholar · View at Scopus
- N. Ramakrishnan, P. B. S. Kumar, and J. H. Ipsen, “Modeling anisotropic elasticity of fluid membranes,” Macromolecular Theory and Simulations, vol. 20, no. 7, pp. 446–450, 2011. View at Publisher · View at Google Scholar · View at Scopus
- H. Noguchi and G. Gompper, “Fluid vesicles with viscous membranes in shear flow,” Physical Review Letters, vol. 93, no. 25, Article ID 258102, 2004. View at Publisher · View at Google Scholar · View at Scopus
- H. Noguchi and G. Gompper, “Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 72, no. 1, Article ID 011901, 2005. View at Publisher · View at Google Scholar · View at Scopus
- V. Vitelli and D. R. Nelson, “Nematic textures in spherical shells,” Physical Review E, vol. 74, no. 2, Article ID 021711, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- R. Rosso, E. G. Virga, and S. Kralj, “Parallel transport and defects on nematic shells,” Continuum Mechanics and Thermodynamics, vol. 24, no. 4–6, pp. 643–664, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- R. D. Kamien, “The geometry of soft materials: a primer,” Reviews of Modern Physics, vol. 74, no. 4, pp. 953–971, 2002. View at Publisher · View at Google Scholar · View at Scopus
- H. Poincaré, “Memoire sur les courbes definies par une equation differentielle,” Journal de Mathématiques Pures et Appliquées, vol. 2, pp. 151–217, 1886. View at Google Scholar
- U. Seifert, K. Berndl, and R. Lipowsky, “Shape transformations of vesicles: phase diagram for spontaneous-curvature and bilayer-coupling models,” Physical Review A, vol. 44, no. 2, pp. 1182–1202, 1991. View at Publisher · View at Google Scholar · View at Scopus
- A. H. Bahrami, M. Raatz, J. Agudo-Canalejo et al., “Wrapping of nanoparticles by membranes,” Advances in Colloid and Interface Science, vol. 208, pp. 214–224, 2014. View at Publisher · View at Google Scholar · View at Scopus
- D. Jesenek, Š. Perutková, W. Góźdź, V. Kralj-Iglič, A. Iglič, and S. Kralj, “Vesiculation of biological membrane driven by curvature induced frustrations in membrane orientational ordering,” International Journal of Nanomedicine, vol. 8, pp. 677–687, 2013. View at Publisher · View at Google Scholar · View at Scopus